Just before the weekend another Sankey diagram for you. One reader suggested I should present a Sankey diagram that contained an Easter egg (without specifying whether he meant flows going in a round, egg-like arrow path or a joke hidden inside the diagram)

Here is one from Japan. It has two loops, and qualifies as a joke too. Just look at the quantities displayed and you know what I mean…

This is from an NTT Technical Review article ‘Development of SOFC Power Generation Module with High Electrical Generation Efficiency’ by Yoshiteru Yoshida, Katsuya Hayashi, and Masayuki Yokoo.

This Sankey diagram of the energy flows (values in kJ/s) is for the SOFC reference case. The wet and dry biomass flows are evaluated using lower heating values, higher heating value (HHV) basis in parentheses.

As you are aware I am constantly looking for samples of Sankey diagrams, be they good, mediocre, or … fair.

This 2009 report on fuel cell technology (‘Natural Gas – Fueled Distributed Generation Solid Oxide Fuel Cell Systems. Projection of Performance and Cost of Electricity’ prepared by J.Thijssen LLC for US Department of Energy, National Energy Technology Laboratory, and RDS under contract number 41817M2846) has two Sankey diagrams I would like to share with you. The report assesses energy efficiency, water use and CO2 emissions of the fuel cell system.

I confess I am no expert in fuel cell technology (Wikipedia basics), and I assume the technology has evolved quite a bit over the last years. So I limit myself to a description of the Sankey diagrams presented.

On page 9 figure 3-4 shows the energy balance “Sankey Diagram of the Baseline NG DG SOFC System” (NG = natural gas, DG = distributed generation, SOFC = solid oxide fuel cell). With an energy content of the natural gas input of 9.1 MW (based on the higher heating value) and an output of 5.2 MW electric energy the system has an efficiency of 57%.
We can identify three loopbacks: syngas is recovered and fed back into the process, and heat is recovered “by thermal recuperation (by preheating the cathode air and raising and superheating steam) and chemical recuperation (by reforming part of the hydrocarbons, mainly methane, in the fuel)” (p. 8). These are the red arrows.

Now here is what I don’t like about the Sankey diagram: While most of the arrows seem to be to scale, some aren’t. Losses branching out to the top are graphically exaggerated. The arrow representing thermal losses (2.5 MW) should be about half as wide as the one for 5.2 MW ‘Net Power AC’.
The heavy spikes at the head of the arrow for inverter losses and energy used for CO2 compression overemphasize the comparatively small quantities of 0.2 MW and 0.3 MW (?!). The latter arrow seems to be labeled incorrectly (30 MW instead of 0.3 MW).

The Sankey diagram for water use of the fuel cell system on page 22 also has some obvious technical flaws:

In this diagram we are looking at water flow rates in kg/s. It seems as if most of the water is in a closed loop (0.52 kg/s) in the syngas recovery. The report on page 21 explains that “[w]hile the water demand for the NGDG system is considerable, net water use for the NGDG system is minor (only about 0.15 gal/kWh or 790 gal/day […]). The steam reformer has a steam demand more than 10 times this amount (about 0.55 kg/s)”. The label of the feed arrow at the top left has a wrong label and refers to 790 gal/hour(!).

The magnitude (width of arrow) of the main loop representing a flow rate of 0.52 kg/s water in syngas recycle is not maintained especially in the curves.
The main problem however is that it is not clear at which process step water comes in or flows out. I have come to the conclusion that the arrows for inflows (increase of arrow width) and outflows/losses (decrease of arrow width) are actually missing. So if you imagine an outward arrow to the label “0.12 kg/s water consumption at SMR” and two inward arrows from “0.44 kg/s water production in stack” and “0.06 kg/s water production in burner” the Sankey diagram starts to make sense.

Will try to draw my own version of the Sankey diagram and present it here. Note that ‘SMR’ is for steam methane reforming, abbreviation not explained in the report.

Using a feed of 8,42 kg natural gas per hour with an energy content of 114,75 KW (based on the lower heating value) the CHP equipment yields 59,5 KW electric energy and heat. Biogas or hydrogen can also be used as fuel.

Electrical efficiency is between 53 and 65% net AC, the total energy efficiency is larger 85%.

From a project summary on the webpage of the Fuel Cell Research Lab at University of Delaware’s Department of Mechanical Engineering comes this Sankey diagram.

This is for a bus operating on the University of Delaware campus. The Sankey diagram shows energy flow and losses in the hybrid power train for a typical drive cycle. Unit is Wh, percentages are given in the labels as additional information. Energy is recovered when braking and is fed back to the battery (see upstream arrow ‘Energy Recovery’).

“The fuel cell system balance of plant consumes a significant fraction of the energy of the hydrogen supplying the stack, so efficiency gains there are potentially quite useful. Most of the balance of plant energy feeds the air compressor, so efficiency could be increased by improving air humidification to allow lower air system backpressure”

Simple black and white diagram with a top-down orientation. The only extra that does not serve to carry information is the schematic road figuring at the bottom….

Cummins Power Generation and Versa Power Systems are teaming in the development of a Solid Oxide Fuel Cell (SOFC). The three-phase SECA project, funded by the DOE/NETL (US DOE SECA DE-FC26-01NT41244) has completed its first phase. A prototype (named Mission 1) has been developed that produced 3.2 kW of electrical power over 1500 hours test operation time, with an availability of 99%. The ultimate goal is to built a SOFC power system that provides 10 kW.

The Sankey diagram below is reproduced (courtesy of the author) from a presentation that summarizes the findings of the first phase of the project.

The Sankey diagram distinguishes chemical energy, thermal energy and electrical energy (as output) and shows the processes reformer, stack and combustor. Some of the heat from combustion can be recovered and used in the reformer. The orange arrow leaving the system at the right should actually be thinner, as 10% branches off. Unfortunately the arrow magnitudes in the diagram are not to scale, as can be seen between stack and reformer, where the magnitude of the chemical energy flow (yellow) is larger than the one of electrical energy (black), even though it is 36 % compared to 39%. The black arrow is also thicker at its tail than at its head.